Assignment 2 Fixed Income
Essay by Pattarapol Hanpatchaiyakul • July 2, 2015 • Coursework • 1,217 Words (5 Pages) • 1,292 Views
CHAPTER 4
2. Calculate the requested measures in parts (a) through (f) for bonds A and B (assume that each bond pays interest semiannually)
(A) What is the price value of a basis point for bonds A and B?
- Bond A
Price (8%) = $100
Price (8.01%)= $99.9819
PVBP = price (8%) – price (8.01%)
PVBP = 100-99.8919 = $0.0181 per $100
- Bond B
Price(8%) = $104.0554
Price (8.01%)= $104.0139
PVBP = price(8%) – price(8.01%)
PVBP = 104.0554 – 104.0139 = $0.0415 per $100
(B) Compute the Macaulay durations for the two bonds.
Bond A
At yield = 8%
t
CF
PVCF
t*PVCF
1
4
3.85
3.85
2
4
3.70
7.40
3
4
3.56
10.67
4
104
88.90
355.60
100.00
377.51
Dmac (Half year)
3.775091
Bond B
t
CF
PVCF
t*PVCF
1
4.5
4.33
4.33
2
4.5
4.16
8.32
3
4.5
4.00
12.00
4
4.5
3.85
15.39
5
4.5
3.70
18.49
6
4.5
3.56
21.34
7
4.5
3.42
23.94
8
4.5
3.29
26.30
9
4.5
3.16
28.45
10
104.5
70.60
705.96
104.06
864.53
Dmac (Half year)
8.308352
Dmac (year)
4.154176
(C) Compute the modified duration for the two bonds.
Bond A
Modified duration = Dmac(years) /(1+YTM/2) = (3.775091/2)/1.04 = 1.815 (years)
Bond B
Modified duration = Dmac(years) /(1+YTM/2) = 4.154176/1.04 = 3.9944 (years)
(D) Compute the approximate duration for bonds A and B using the shortcut formula by changing yields by 20 basis points and compare your answers with those calculated in part (c).
Approximate duration = (P_ - P+)/2P0(dy)
Bond A
Price changes when yield increases by 20 bps (P+)
= -PVBP*(change in yield) = -$0.0181*20 = -$0.3620
So, P+ = 100 – 0.3620 = $99.6380
Price changes when yield decreases by 20 bps (P_)
= -PVBP*(change in yield) = -$0.0181*(-20) = $0.3620
So, P- = 100 + 0.3620 = $100.362
The approximate duration = (100.362 – 99.638)/2*100*(0.002) = 1.81
Bond B
yield increases by 20 bps
= -PVBP*(change in yield) = 0.0415 *20 = -0.83
So, P+ = 104.0554 – 0.83 = 103.2254
yield decreases by 20 bps
= -PVBP*(change in yield) = -0.0415 *(-20) = $0.83
So, P_ = 104.0554 + 0.83 = 104.8854
The approximate duration = (104.8854 – 103.2254)/2*104.0554*(0.002) = 3.9885
The approximate durations are a bit lower than the duration calculated using the formula.
3. Can you tell from the following information which of the following three bonds will have the greatest
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